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Standardized Test Preparation and
Tips for Success

Preparing Your Students for the
Ohio Graduation Test in Mathematics

Strand Resources:
Number, Number Sense, and Operations

Ohio Graduation Test Prep Gif

CT4ME has identified resources related to each benchmark of the Ohio Mathematics Academic Content Standards that students should have mastered by the end of the grades 8-10 program.

Identify the benchmark (A-I) for review in Number, Number Sense, and Operations. Below the benchmark, you will find Web resources for reviewing the concept and practice problems.

Students should be able to review on their own using these resources. If you are not an Ohio educator, these resources can still benefit your test prep efforts, as benchmarks in other states are similarly stated.

Download the Test Prep Strand Booklet

Number, Number Sense and Operations (pdf) This test prep booklet (about 200 KB) is designed to help you monitor your progress toward mastery of each benchmark in this strand. You can print the entire booklet, or just those pages for benchmarks you need to work on. Write notes in the booklet next to each resource you use in your review.

If needed, download Adobe Acrobat Reader, free software for viewing and printing PDF files.

You might need to download Java, a free plug-in from Sun Microsystems to interact with virtual manipulatives on this page.

Other strand resources:

[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ] [ Mathematical Processes ]

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How shall we interpret Number?

Numbers are used for math computations in the real number system.

Map of Egypt

Here's a bit of history for you!

Egyptian Math--Numbers

Imagine writing your numbers with seven different symbols: a single stroke, a hobble for cattle, a coil of rope, a lotus plant, a finger, a tadpole or frog, or a god with his arms raised above his head. Read more on this topic from Mark Millmore and explore doing a few problems with Egyptian Math.

Benchmarks for Number, Number Sense, and Operations

Benchmarks in this strand have been correlated to the Common Core State Standards (CCSS) for Mathematics for the Conceptual Category (CC), Domain (D), and Cluster (C).

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NOTE: As a general resource for all Number Sense and Operations strand benchmarks, students and teachers might consult the following resources:

Algebra from Oswego City School District (NY) Regents Exam Prep Center. Each sub-section includes lessons and interactive practice exercises. See problems in number theory and operations. There is also a pre-algebra review of rational/irrational numbers, order of operations, and signed numbers.
Number and Operations from LearningMath.org contains 10 sessions each about 2.5 hours long with videos, online and print-based problem solving activities, interactive activities and demonstrations.

A. Use scientific notation to express large numbers and numbers less than one.

CCSS: CC: grade 8, D: Expressions and Equations, C: Work with radicals and integer exponents.

AlgebraLab.org: Scientific Notation Introduction and practice exercises converting to scientific notation and decimal notation from the scientific form.

West Texas A&M University Virtual Math Lab College Algebra Tutorial: Scientific Notation: How to write numbers in scientific notation, perform multiplication and division with video explanations and practice problems.

Oswego City School District (NY), Regents Prep, Algebra section: Scientific Notation

Math and Science Activity Center from Edinformatics.com: Scientific Notation Problem Generator. Randomly generated problems in either scientific notation or standard notation representation of a number will be shown. Fill in the blanks, then check answer.

Mercer County Community College, Debbie Kell, multiple choice practice: Converting between standard and scientific notation, performing operations, significant digits, applications

QuickMath.com: Scientific Notation. Enter your number and see detailed explanation of a conversion.

Play the video tutorial at the Ohio Resource Center for Mathematics, Science, and Reading:

Scientific Notation: Basics for writing numbers in scientific notation, video #1.

B. Identify subsets of the real number system.

Edmonton Public Schools (CA), Jim Reed, Math 9 is the general resource for grade 9. See Number Systems: Demonstration of the subsets of the real number system, then test your understanding with the interactive Number System Muncher.

Oswego City School District (NY) Intermediate Test Prep Center Math 7; Interactive, Lesson and Practice:

Distinguish Subsets of Real Number System

Recognize the difference between rational and irrational numbers

Oswego City School District (NY), Regents Prep, Algebra section: Rational and Irrational Numbers -- a review topic from pre-algebra.

Math Forum, Dr. Math FAQ: Integers, Rational, and Irrational Numbers

Play video at PilotMath.com for Real Numbers:

Pilot Math Number Systems and Variables Cartoon format with students. Uses Venn diagrams to illustrate the subsets of the real number system.

C. Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

CCSS: CC: Algebra, D: Arithmetic with Polynomials and Rational Expressions, C: Perform arithmetic operations on polynomials.

Maths Online Interactive Test: Number Sets (multiple choice with more than one answer).

Purple Math: Order of Operations (PEMDAS) Lesson with worked examples.

Math.com: Order of Operations with more than one operation. Lesson, worked examples, and practice problems.

Oswego City School District (NY), Regents Prep, Algebra section: Order of Operations and Evaluating Expressions practice problems.

West Texas A&M University, Intermediate Algebra Tutorials: Operations on Real Numbers, practice with answers, and additional related links

Oswego City School District (NY), Regents Prep, Algebra section: Properties of Real Numbers

Play videos at YouTube.com for Real Numbers:

Fundamental Definitions and Notations: Focus on order of operations

Arithmetic of Real Numbers. Using six problems, the presenter reviews addition/subtraction of integers, order of operations, distributive property, combining like terms.

D. Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.

CCSS: CC: grade 8, D: Number System, C: Know that there are numbers that are not rational, and approximate them by rational numbers.

Math Forum, Dr. Math FAQ: Rational Numbers, and Irrational Numbers

The Math Page, Real Numbers:

Rational Numbers

Irrational Numbers

Oswego City School District (NY), Regents Prep, Algebra section: Rational and Irrational Numbers, including approximations of irrational numbers. Lesson and practice problems.

E. Compare, order and determine equivalent forms of real numbers.

CCSS: CC: grade 7, D: Number System, C: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

CCSS: CC: grade 7, D: Expressions and Equations, C: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

CCSS: CC: grade 8, D: Number System, C: Know that there are numbers that are not rational, and approximate them by rational numbers.

Math Forum, Dr. Math FAQ: Explanation for converting fractions, decimals, and percents

AAA Math: Comparing and equivalent forms (rational numbers) with online practice

Glencoe Online Study Tools, Pre-Algebra, multiple choice practice: Rational numbers (equivalent forms and subsets)

F. Explain the effects of operations on the magnitude of quantities.

NCTM Principles and Standards for School Mathematics E-examples: Learning about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures has two parts:

Side Length and Area of Similar Figures

Side Length, Volume, and Surface Area of Similar Solids

G. Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

CCSS: CC: Geometry, D: Circles, C: Find arc lengths and areas of sectors of circles.

Algebra Help: Proportion Basics

AlgebraLab.org:

Rates and Ratios study aids and practice problems.

Word Problem Exercises using simple proportions to solve five problems with real-life scenarios. Fill in the blank.

The Math Page, Skill in Arithmetic: Percent increase or decrease problems with answers

Mercer County Community College, Debbie Kell: Proportions interactive multiple choice quiz with rate, ratio, proportions, problem solving

Glencoe Online Study Tools, Pre-Algebra, multiple choice practice:

Using the percent proportion

Using percent equations

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice:

Ratios and Proportions

Percent of Change

Shodor.org: Percents

H. Find the square root of perfect squares, and approximate the square root of non-perfect squares.

CCSS: CC: grade 8, D: Expressions and Equations, C: Work with radicals and integer exponents.

How to calculate a square root without a calculator

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice: Square Roots and Real Numbers

Algebrahelp.com: Perfect Squares Chart

I. Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

CCSS: CC: grade 8, D: Expressions and Equations, C: Work with radicals and integer exponents.

Institute for Energy and Environmental Research: Scientific Notation Review and Practice Worksheet with answers

University of Oregon, Davison Soper: Scientific Arithmetic, explanation and multiple choice practice

Glencoe Online Study Tools, Geometry Concepts and Applications 2004, multiple choice practice: Simplifying Square Roots

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice: Compute with Scientific Notation

Oswego City School District (NY), Regents Prep, Algebra section:

Operations with Radicals

Exponents

Play the video tutorials at the Ohio Resource Center for Mathematics, Science, and Reading:

Scientific Notation: Computation for computing with scientific notation, using significant digits, and explaining the meaning of precision and accuracy, video #2.

Exponents for understanding exponents and using the rules for computation, video #20.